Random Assembly of Logical Elements

Abstract

Since the notion of random and randomness repeatedly arises in the field we are discussing, I thought that maybe it would be of some interest to build examples of what may happen in certain circumstances when one is using random operations.

The following quotation from page 42 of “Finality and Form” by Warren & McCulloch (published 1952 by Thomas of Springfield, Illinois) well illustrates the value of the present paper to the theme of this symposium, despite the author’s modest insistence that he was not presenting any model.—Ed.

“All learning, including the process whereby the rules of induction are perfected, orders step by step an ensemble erstwhile chaotic. And, whenever this, which is a change of state, happens to an ensemble, the statistical variables that characterize it no longer require merely the first few members of the probability-distributions of monads, diads, triads, etc. of the elements of its component systems, but, instead, depend upon the ultimate trends of these distributions of n-ads as n increases without limit. For no task in physics is our mathematics so feeble or so far to seek: Fortunately for us, this change of state in our brains that may happen to water in a moment of freezing, goes merrily on in us as long as we can learn, and some of us may live to share the fun of concocting the required mathematics.”

Because the author was unable, by reason of many demands on his time, to submit this paper in written form, his oral presentation is here given in abridged transcription from magnetic tape. —Ed.